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arXiv:2601.09115

A saturation-absorption rubidium magnetometer with multilevel optical Bloch-equation modeling for intermediate-to-high fields

Mayand Dangi, Prateek Rajan Gupta, Joseph Kasti, Nivedan Vishwanath, Michael Zepp, David Smith, Benedikt Geiger, Jennifer T. Choy

quant-phphysics.atom-phSubmitted Jan 14, 2026• Announced Jan 15, 2026• 0 citations
v1 · Jan 14, 2026v2 · Jun 10, 2026
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Abstract

We present SASHMAG (Saturated Absorption Spectroscopy High-field MAGnetometer), an atomic sensor designed for precision magnetic-field measurements in the intermediate-to-high field regime ($>0.2\,\text{T}$) using Rubidium-87 ($^{87}Rb$). The sensor operates in the hyperfine Paschen-Back regime, where the hyperfine and Zeeman interactions decouple, and utilizes counter-propagating pump-probe configuration in Faraday geometry to resolve isolated, Doppler-free Zeeman transitions. To interpret the resulting spectra in this strongly field-dependent regime, we developed a comprehensive multilevel optical Bloch-equation model solved explicitly in the uncoupled $\ket{m_I, m_J}$ basis, capturing state mixing and nonlinear saturation dynamics. This model reproduces measured spectra at sub-Doppler resolution and is consistent with analytical expectations for power broadening and thermal Doppler scaling. Magnetic field estimation is performed using a physics-constrained optimization routine that infers the magnetic field by minimizing the residual between experimentally extracted line centers and calculated transition frequencies from the field-dependent Hamiltonian. We demonstrate magnetic field retrieval from $0.2\,\text{T}$ to $0.4\,\text{T}$ with a precision of $\pm 0.0017 \,\text{T}$). Furthermore, the validated simulation establishes a foundation for generating synthetic training datasets, paving the way for autonomous, Machine Learning-enhanced magnetometry in applications ranging from MRI to fusion reactors.

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We use a magnetometer probe based on the Zeeman shift of the rubidium resonant optical transition to explore the atomic magnetic response for a wide range of field values. We record optical spectra for fields from a few tesla up to 60 T, the limit of the coil producing the magnetic field. The atomic absorption is detected by the fluorescence emissions from a very small region with a submillimeter size. We investigate a wide range of magnetic interactions from the hyperfine Paschen-Back regime to the fine one and the transitions between them. The magnetic field measurement is based on the rubidium absorption itself. The rubidium spectroscopic constants were previously measured with high precision, except the excited state Land\'e ggg-factor that we derive from the position of the absorption lines in the transition to the fine Paschen-Back regime. Our spectroscopic investigation, even if limited by the Doppler broadening of the absorption lines, measures the field with a 20 ppm uncertainty at the explored high magnetic fields. Its accuracy is limited to 75 ppm by the excited state Land\'e ggg-factor determination.
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39 K atoms have the smallest ground state ( 2 S 1 / 2 ) hyperfine splitting of all the most naturally abundant alkali isotopes and, consequently, the smallest characteristic magnetic field value B 0 = A 2 S 1 / 2 / μ B ≈ 170 G , where A 2 S 1 / 2 is the ground state’s magnetic dipole interaction constant. In the hyperfine Paschen–Back regime ( B ≫ B 0 , where B is the magnitude of the external magnetic field applied on the atoms), only eight Zeeman transitions are visible in the absorption spectrum of the D 1 line of 39 K , while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of 39 K , this behavior is reached already at relatively low magnetic field B > B 0 . For each circular polarization ( σ − , σ + ), four spectrally resolved atomic transitions having sub-Doppler widths are recorded using a sub-microsized vapor cell of thickness L = 120 − 390 n m . We present a method that allows to measure the magnetic field in the range of 0.1 − 10 k G with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with large gradients (up to 3 G/µm). The theoretical model describes well the experimental results.
We perform saturated absorption spectroscopy on the D2{D}_{2}D2​ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05--0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a V\mathsf{V}V configuration, and on four-level systems in an N\mathsf{N}N or double-N\mathsf{N}N configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-N\mathsf{N}N crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.
We perform saturated absorption spectroscopy on the D2_22​ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05-0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a V configuration and on four-level systems in a N or double-N configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-N crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.